REGRESSION METHODS FOR INTERVAL-VALUED VARIABLES IN ASSET PRICING

Financial data are often affected by uncertainty: imprecision, incompleteness, etc. Therefore in a decision making problem, we should be able to process uncertain information. The uncertainty in the data may be treated by considering, rather than a single value, the interval of values in which the data may fall. It is known that the Capital Asset Pricing Model (CAPM) [1] provides an expression which relates the expected return of an asset to its systematic risk. The extension of the CAPM to the case in which the returns of any considered asset and of the market portfolio are interval-valued variables (IntervalCAPM) has been introduced in [2]. The purpose of the present work is first to describe some regression methodologies for interval-valued variables already present in the literature, and second to compare those different methodologies in the framework of the IntervalCAPM. A real financial case is analyzed, and the numerical results using the different methodologies are compared to one another, the interval regression method Iregr [3], with respect to other interval regression methods ([4], [5], [6]), shows some good advantages well described in the present work.